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Simplifying -4y2 + 24y + 48 = 0 Reorder the terms: 48 + 24y + -4y2 = 0 Solving 48 + 24y + -4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(12 + 6y + -1y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(12 + 6y + -1y2)' equal to zero and attempt to solve: Simplifying 12 + 6y + -1y2 = 0 Solving 12 + 6y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12 + -6y + y2 = 0 Move the constant term to the right: Add '12' to each side of the equation. -12 + -6y + 12 + y2 = 0 + 12 Reorder the terms: -12 + 12 + -6y + y2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -6y + y2 = 0 + 12 -6y + y2 = 0 + 12 Combine like terms: 0 + 12 = 12 -6y + y2 = 12 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = 12 + 9 Reorder the terms: 9 + -6y + y2 = 12 + 9 Combine like terms: 12 + 9 = 21 9 + -6y + y2 = 21 Factor a perfect square on the left side: (y + -3)(y + -3) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (y + -3) equal to 4.582575695 and -4.582575695.Subproblem 1
y + -3 = 4.582575695 Simplifying y + -3 = 4.582575695 Reorder the terms: -3 + y = 4.582575695 Solving -3 + y = 4.582575695 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 4.582575695 + 3 Combine like terms: -3 + 3 = 0 0 + y = 4.582575695 + 3 y = 4.582575695 + 3 Combine like terms: 4.582575695 + 3 = 7.582575695 y = 7.582575695 Simplifying y = 7.582575695Subproblem 2
y + -3 = -4.582575695 Simplifying y + -3 = -4.582575695 Reorder the terms: -3 + y = -4.582575695 Solving -3 + y = -4.582575695 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -4.582575695 + 3 Combine like terms: -3 + 3 = 0 0 + y = -4.582575695 + 3 y = -4.582575695 + 3 Combine like terms: -4.582575695 + 3 = -1.582575695 y = -1.582575695 Simplifying y = -1.582575695Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.582575695, -1.582575695}Solution
y = {7.582575695, -1.582575695}
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